WAEC Mathematics Past Questions & Answers - Page 210

1,046.

PQRS is a trapezium in which |PS| = 9cm, |QR| = 15cm, |PQ| = \(2\sqrt{3}, \angle PQR = 90^o and \angle QRS = 30^o\). Calculate the area of the trapezium

A.

\(24\sqrt{3} cm^2\)

B.

\(36\sqrt{3} cm^2\)

C.

\(42\sqrt{3} cm^2\)

D.

\(72\sqrt{3} cm^2\)

Correct answer is A

No explanation has been provided for this answer.

1,047.

A solid cylinder of radius 7cm is 10 cm long. Find its total surface area.

A.

\(70\pi cm^2\)

B.

\(189\pi cm^2\)

C.

\(210\pi cm^2\)

D.

\(238\pi cm^2\)

Correct answer is D

S = \(2\pi r^2 + 2\pi rh\)

= \(2\pi r(r + h)\)

= \(2\pi (7) (7 + 10)\)

= \(238\pi cm^2\)

1,048.

The diagram shows a triangular prism of length 7cm. The right - angled triangle PQR is a cross section of the prism |PR| = 5cm and |RQ| = 3cm. What is the volume of the prism?

A.

28cm2

B.

42cm2

C.

70cm2

D.

84cm2

Correct answer is B

Volume of prism = Area x height

In \(\Delta\) RQP, QR\(^2\) + QP\(^2\) = RP\(^2\)

3\(^2\) + QP\(^2\) = 5\(^2\)

QP\(^2} = 5\(^2\) - 3\(^2\)

QP = \(\sqrt{16}\)

= 4 cm 

\(\therefore\) Area = \(\frac{1}{2} \times base \times height\)

= \(\frac{1}{2} \times 3 \times 4\)

= 6 cm\(^2\)

Volume = 6 x 7

= 42 cm\(^3\)

1,049.

The diagram shows a triangular prism of length 7cm. The right-angled triangle PQR is a cross-section of the prism |PR| = 5cm and |RQ| = 3cm. What is the area of the cross-section?

A.

4cm2

B.

6cm2

C.

15cm2

D.

20cm2

Correct answer is B

In \(\Delta\) RQP, QR\(^2\) + QP\(^2\) = RP\(^2\)

3\(^2\) + QP\(^2\) = 5\(^2\)

QP\(^2} = 5\(^2\) - 3\(^2\)

QP = \(\sqrt{16}\)

= 4 cm 

\(\therefore\) Area = \(\frac{1}{2} \times base \times height\)

= \(\frac{1}{2} \times 3 \times 4\)

= 6 cm\(^2\)

1,050.

In the diagram, MN||PQ, |LM| = 3cm and |LP| = 4cm. If the area of ∆LMN is 18cm2, find the area of the quadrilateral MPQN

A.

3cm2

B.

6cm2

C.

14cm2

D.

24cm2

Correct answer is C

\(\frac{LM}{LP} = \frac{3}{4}\)

\(\frac{Area of LMN}{Area of LPQ} = \frac{3^2}{4^2}\)

Area of LPQ = \(\frac{16}{9}\times 18 = 32 cm^2\)

Area of quadrilateral MPQN = 32 – 18 = \(14 cm^2\)